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OctInsertion Sort for Nearly Sorted Array
Insertion Sort for Nearly Sorted Array
The Insertion Sort Algorithm is a simple comparison-based sorting algorithm that builds the sorted array one element at a time by inserting each element into its correct position in the sorted portion of the array. It is particularly efficient for nearly sorted arrays, where elements are close to their final positions, requiring fewer comparisons and shifts. This makes it ideal for scenarios where the input is already partially sorted.
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Example:
- Input: nums = [2, 1, 3, 5, 4, 6] (nearly sorted)
- Output: [1, 2, 3, 4, 5, 6]
- Explanation: The array is sorted in ascending order.
Logic
Enter an array of numbers (comma-separated) to sort it using the Insertion Sort algorithm.
Program (Python - Insertion Sort Implementation)
The following Python code implements the Insertion Sort algorithm with O(n²) time complexity in the worst case, but it performs close to O(n) for nearly sorted arrays, where n is the length of the array.
def insertionSort(nums):
for i in range(1, len(nums)):
key = nums[i]
j = i - 1
# Shift elements that are greater than key to the right
while j >= 0 and nums[j] > key:
nums[j + 1] = nums[j]
j -= 1
# Place key in its correct position
nums[j + 1] = key
return nums
# Example usage
nums = [2, 1, 3, 5, 4, 6]
print(insertionSort(nums)) # Output: [1, 2, 3, 4, 5, 6]
Output
For the input nums = [2, 1, 3, 5, 4, 6], the output is:
[1, 2, 3, 4, 5, 6]
Explanation:
The nearly sorted array is sorted in ascending order using the insertion sort algorithm.
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